A capacitor has 7 parallel plates separated by sheets of mica 0.5mm thick and a relative permittivity of 6…

Question

A capacitor has 7 parallel plates separated by sheets of mica 0.5mm thick and a relative permittivity of 6. The capacitor whose area of each plate is 500 cm 2 is connected to a 400V supply, Calculate the; i Capacitance of the capacitor ii Charge in the capacitor (Eo = 8.85 × 10⁻¹² fm⁻¹)

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Here are the calculations for the capacitor:

Identify the given values and convert them to SI units.
- Number of parallel plates, $N = 7$
- Thickness of mica sheets, $d = 0.5 \, \text{mm} = 0.5 \times 10^{-3} \, \text{m}$
- Relative permittivity of mica, $\epsilon_r = 6$
- Area of each plate, $A = 500 \, \text{cm}^2 = 500 \times (10^{-2})^2 \, \text{m}^2 = 0.05 \, \text{m}^2$
- Voltage supply, $V = 400 \, \text{V}$
- Permittivity of free space, $\epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m}$
Determine the number of effective dielectric layers.
For a capacitor with $N$ parallel plates, there are $N-1$ effective dielectric layers.
Number of effective layers, $n = N-1 = 7-1 = 6$ .
Calculate the capacitance of the capacitor.
The formula for the capacitance of a multi-plate capacitor is:
$C = (N-1) \frac{\epsilon_r \epsilon_0 A}{d}$
Substitute the values:
$C = 6 \times \frac{6 \times 8.85 \times 10^{-12} \, \text{F/m} \times 0.05 \, \text{m}^2}{0.5 \times 10^{-3} \, \text{m}}$ $C = 6 \times \frac{2.655 \times 10^{-12} \, \text{F}}{0.5 \times 10^{-3}}$ $C = 6 \times 5.31 \times 10^{-9} \, \text{F}$ $C = 31.86 \times 10^{-9} \, \text{F}$ $C = 31.86 \, \text{nF}$
The capacitance of the capacitor is $\boxed{\text{31.86 nF}}$ .
Calculate the charge in the capacitor.
The formula for charge is $Q = CV$ .
Substitute the calculated capacitance and the given voltage:
$Q = 31.86 \times 10^{-9} \, \text{F} \times 400 \, \text{V}$ $Q = 12744 \times 10^{-9} \, \text{C}$ $Q = 1.2744 \times 10^{-5} \, \text{C}$
The charge in the capacitor is $\boxed{\text{1.2744} \times 10^{-5} \, \text{C}}$ .

A capacitor has 7 parallel plates separated by sheets of mica 0.5mm thick and a relative permittivity of 6. The capacitor whose area of each plate is 500 cm 2 is connected to a 400V supply, Calculate the; i Capacitance of the capacitor ii Charge in the capacitor (Eo = 8.85 x 10⁻¹² fm⁻¹)

Answer

Step-by-step solution

Identify the given values and convert them to SI units.

Determine the number of effective dielectric layers.

Calculate the capacitance of the capacitor.

Calculate the charge in the capacitor.

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